CN113190957A - Controllable source electromagnetic simulation wave number sequence optimization method based on elimination strategy - Google Patents
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Abstract
The invention provides a controllable source electromagnetic simulation wave number sequence optimization method based on an elimination strategy, which comprises the following steps: initializing an input variable; adjusting the positions of wave number sequence nodes based on a least square fitting method; eliminating redundant wave numbers at the minimum spacing position by using an optimized wave number algorithm I; eliminating redundant wave numbers of non-minimum spacing positions by using an optimized wave number algorithm II; judging whether the optimized wave number sequence is the same as the initial wave number sequence or not; and outputting the final optimized wave number sequence. Compared with the traditional wave number sequence obtained by logarithmically equally-spaced acquisition, the obtained optimized wave number sequence has more reasonable position distribution, and on the premise of obtaining the same calculation precision, the number of nodes is less, so that the speed and the operation efficiency of simulation calculation can be improved. Compared with the existing optimized wave number algorithm, the algorithm provided by the invention has the characteristics of high calculation speed and high efficiency, and is suitable for the simulation of a complex resistivity anisotropy model.
Description
Technical Field
The invention relates to the technical field of marine geophysical numerical simulation, in particular to a controllable source electromagnetic simulation wave number sequence optimization method based on an elimination strategy.
Background
The Controlled Source Electromagnetic Method (CSEM) is a geophysical method widely used for resource exploration. A large amount of model simulation operation is needed to be carried out during the processing, inversion and explanation of the electromagnetic data of the controllable source, and the realization process of the model simulation operation involves the conversion of solution domain, such as wave number-space domain conversion and the like. Aiming at the problems of complex anisotropic laminar medium simulation and 2.5-dimensional numerical simulation, the wave number-space domain conversion is realized by utilizing a digital filtering algorithm after calculating the response corresponding to the wave number sequence. Thus, the number and distribution of wavenumbers in the wavenumber sequence are important factors affecting the calculation accuracy and the speed of the algorithm. In order to ensure the calculation accuracy of the simulation result, the conventional wave number sequence is obtained by performing dense logarithmic equally-spaced sampling within a certain numerical range, however, the wave number sequence selected in this way has more redundant nodes, thereby reducing the calculation efficiency of the simulation. Therefore, the wave number sequence with the node number as small as possible and reasonable distribution is obtained under the condition of ensuring reasonable calculation precision, the calculation speed of simulation can be improved to a great extent, and the calculation efficiency is improved.
In the geophysical literature, few researches on the selection of an optimized wave number sequence are carried out, and Xueshi (1988) calculates the discrete wave number by using an optimization method in the process of solving a direct-current point source two-dimensional electric field problem, and each electrode distance of an electrode distance sequence is involved in calculation by the method, so that the calculation result of inverse Fourier transform is optimized finally. Liujian Xin (2005) improved the algorithm proposed in Xueshi, by using the method of calculating geometric discrete wave numbers to give initial values of wave numbers and calculating the partial derivatives of Fourier potentials with respect to wave numbers analytically. The wave number sequence obtained by the method is only the optimal wave number sequence in the direct current method, and the calculation precision requirement of the ocean controllable source electromagnetic forward modeling cannot be met. Shenjinsong (2008) analyzes the influence of the optimized value range and the value points of wave numbers on the numerical simulation result of the two-dimensional frequency domain in the numerical simulation of the frequency domain electromagnetic response in the two-dimensional medium, and considers that the selection and the value of the wave number sequence range have great influence on the numerical simulation result, however, a specific optimal wave number selection method is not provided.
Disclosure of Invention
The invention aims to provide a controllable source electromagnetic simulation wave number sequence optimization method based on an elimination strategy, which can improve the calculation efficiency of controllable source electromagnetic simulation.
In order to achieve the above purpose, the invention provides the following technical scheme:
1. a controllable source electromagnetic simulation wave number sequence optimization method based on an elimination strategy is characterized by mainly comprising the following steps:
s1, initializing input variables including an initial wave number sequence and error precision;
s2, adjusting the positions of wave number sequence nodes based on a least square fitting method, and outputting a preliminary solution;
s3, eliminating redundant wave number at the minimum distance position by using the first optimized wave number algorithm;
s4, eliminating redundant wave numbers at positions with non-minimum spacing positions by using an optimized wave number algorithm II, and outputting an optimized wave number sequence;
s5, judging whether the optimized wave number sequence is the same as the initial wave number sequence or not, if not, turning to S6, if so, adding 1 to the number of wave number nodes, and turning to S2;
s6, outputting a final optimized wave number sequence;
2. the elimination-strategy-based controllable-source electromagnetic simulation wave-number sequence optimization method of claim 1, wherein phi | (d-f (w)) | (| n silica) is calculated based on a least square fitting method2Is an objective function (where phi is the objective function of the optimized wave number; d ═ d1，d2，…，dN)TIs target data; n is the number of data; w ═ w (w)1，w2，…，wM)TThe wave number sequence is adopted, and M is the number of elements in the wave number sequence; f (w) is a model simulation response function), the response of wave number calculation and the minimum value problem of target data are solved, the optimal solution of the objective function phi is solved by a Gaussian-Newton method, namely, the position of each node of the wave number sequence is adjusted in the process, and an initial solution is output;
3. the elimination-strategy-based controllable-source electromagnetic simulation wave number sequence optimization method of claim 1, wherein the wave number algorithm is optimized, wherein based on the aggregation property of redundant nodes, two nodes with the minimum distance in the wave number sequence are found, and the redundant nodes are eliminated under the condition of meeting the precision;
4. the elimination strategy-based controllable source electromagnetic simulation wave number sequence optimization method of claim 1, wherein the second optimization wave number algorithm is to eliminate redundant nodes at non-minimum spacing positions, judge and selectively eliminate each node in the wave number sequence one by one, and finally output the optimized wave number sequence.
Compared with the prior art, the method provided by some embodiments of the invention has the beneficial effects that:
the invention mainly aims at the problem that the calculation efficiency is low possibly caused by wave number sequence redundancy in the ocean source control electromagnetic simulation problem, and provides a controllable source electromagnetic simulation wave number sequence optimization method based on a elimination strategy, wherein the method adjusts the relative position between wave number nodes in a wave number sequence by solving the problem of minimal values of response and target data of optimized wave number calculation; and based on the redundant wave number elimination strategy, eliminating the redundant wave number step by step through the first optimized wave number algorithm and the second optimized wave number algorithm, and finally obtaining an optimized wave number sequence. Compared with the traditional wave number sequence obtained by logarithmically equally-spaced acquisition, the obtained optimized wave number sequence has more reasonable position distribution, and on the premise of obtaining the same calculation precision, the number of nodes is less, so that the speed and the operation efficiency of simulation calculation can be improved. Compared with the existing optimized wave number algorithm, the algorithm provided by the invention has the characteristics of high calculation speed and high efficiency, and is suitable for anisotropic geoelectrical model simulation of complex resistivity.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise.
FIG. 1 is a block flow diagram of the process of the present invention;
FIG. 2 is a structural diagram of a one-dimensional resistivity anisotropy model;
FIG. 3 is a diagram showing the distribution of the initial wavenumber sequence, the preliminary solution, the optimized wavenumber sequence, and the wavenumber sequence obtained by the conventional method;
FIG. 4a shows the calculated horizontal electric field component E in the spatial domain for different wavenumber sequencesy(x, y, z), horizontal magnetic field component Hx(x, y, z) and a vertical electric field component Ez(x, y, z) amplitude contrast diagram;
FIG. 4b shows the calculated horizontal electric field component E in the spatial domain for different wavenumber sequencesy(x, y, z), horizontal magnetic field component Hx(x, y, z) and a vertical electric field component Ez(x, y, z) phase contrast diagram;
FIG. 4c shows the calculated horizontal electric field component E in the spatial domain for different wavenumber sequencesy(x, y, z), horizontal magnetic field component Hx(x, y, z) and a vertical electric field component Ez(x, y, z) amplitude versus error diagram;
FIG. 4d shows the calculated horizontal electric field component E in the spatial domain for different wavenumber sequencesy(x, y, z), horizontal magnetic field component Hx(x, y, z) and a vertical electric field component EzAnd (x, y, z) phase absolute error comparison diagram.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
The invention provides a controllable source electromagnetic simulation wave number sequence optimization method based on a elimination strategy, which is characterized in that the method comprises the steps of solving the problem of minimum values of electromagnetic field response and target data of optimized wave number simulation, adjusting the relative position of each node of a wave number sequence, eliminating redundant wave numbers step by step through a first optimized wave number algorithm and a second optimized wave number algorithm based on the elimination strategy of redundant wave numbers, and finally obtaining an optimized wave number sequence. Therefore, the optimized wave number sequence consisting of a small number of wave number nodes is utilized to obtain a simulation result with high precision, and the speed and the operation efficiency of simulation calculation are greatly improved.
Referring to fig. 1, a controllable source electromagnetic simulation wave number sequence optimization method based on an elimination strategy mainly includes the following steps:
s1: input variables are initialized, including the initial wavenumber sequence and error accuracy.
S2: and adjusting the positions of the wave number sequence nodes based on a least square fitting method, and outputting a preliminary solution.
The objective of the least squares based fitting method is to maximize the fit of the response calculated by the simulation of the selected optimized wavenumber sequence to the target data. Thus, the fitting difference φ of the target data to the forward response is set as the objective function:
φ＝||(d-F(w))||2
in the formula, phi is an optimized wave number objective function; d-f (w) is a residual vector; d ═ d (d)1，d2，…，dN)TIs target data; n is the number of data; w ═ w1，w1，…，wM-is a sequence of wavenumbers; m is the number of elements in the wave number sequence; f (w) is a model simulation function.
When the initial wave number is calculated by using a least square method, a nonlinear simulation function F (w) is linearized, quadratic terms and higher-order terms are ignored in Taylor expansion, and then iteration is carried out to gradually converge towards a real model. Putting the simulation function F (w) at the known wave number node wiAnd (3) processing first-order expansion:
F(wi+1)＝F(wi)+JwΔw
in the formula, JwBeing the Jacobian matrix (the partial derivative of the simulation function F (w) with respect to the wave number sequence w), Δ w is the update quantity of the wave number sequence.
From this, the wave number series type update quantity can be obtained
Wherein k represents the kth inversion iteration; w is akAnd wk+1For the k-th and k + 1-th inversion of the wave number sequence w, Δ wkAnd (5) iterating the wave number sequence for the k-th inversion. Gradient (g) of the objective functionk) And Hessian matrix (H)k) Is as followsForm(s) of
In the optimization iteration process, the precision of the simulation result obtained by calculating the optimized wave number sequence is gradually converged to an accurate solution, and the fitting difference between the simulation result and target data approaches to 0. The present patent uses the following formula to evaluate the rationality of the wave number sequence w. The fitting difference between the simulation result and the target data can be determined by calculating whether the tolerance requirement is met or not according to the following formula:
||e||∞＝maxj＝1，2，…，N|dj-Fj(w)|＜ε
wherein | × | non-conducting phosphor∞D-f (w) is an infinite norm, and e is a residual vector; d ═ d (d)1，d2，…，dN)TIs target data; n is the number of data; w is a sequence of wave numbers; f (w) is a model simulation function; ε is the error accuracy. The above formula tolerance determination method ensures that the maximum error of the electromagnetic field response calculated by the beam sequence satisfying the tolerance requirement is less than the required error accuracy.
S3: and eliminating redundant wave numbers at the minimum spacing position by using the first optimized wave number algorithm.
Considering the aggregation property of the redundant nodes, the first proposed optimized wave number algorithm can be divided into the following 4 steps by finding two nodes with the minimum distance in the wave number sequence and eliminating the redundant nodes under the condition of meeting the precision.
Step 1: searching two nodes n with minimum adjacent spacing(s) in wave number sequence w1And n2；
Step 2: eliminating node n1Obtaining a new wave number sequence w1Verification of tolerance requirement (. epsilon.)1) And calculate w1Minimum adjacent spacing(s)1) (ii) a Eliminating node n2Obtaining a new wave number sequence w2Verification vesselDifference requirement (epsilon)2) And calculate w2Minimum adjacent spacing(s)2)；
And step 3: (1) if w1And w2All satisfy the tolerance requirements, and s1Is less than s2Then n is eliminated from w1Let w be w1And turning to step 1; (2) if w1And w2All satisfy the tolerance requirements, and s1Greater than s2Then n is eliminated from w2Let w be w2And turning to step 1; (3) if there is only w1Satisfy the tolerance requirement, n is eliminated from w1Let w be w1And turning to step 1; (4) if there is only w2Satisfy the tolerance requirement, n is eliminated from w2Let w be w2And turning to step 1; (5) if w1And w2All the requirements of tolerance are not met, and the step 4 is switched to;
and 4, step 4: and outputting the wave number sequence.
S4: and eliminating redundant wave numbers at positions with non-minimum spacing by using the second optimized wave number algorithm, and outputting an optimized wave number sequence.
The optimization algorithm 1 can remove those redundant nodes with the minimum distance in the wave number sequence w, however, there are redundant nodes at positions with non-minimum distance, so the optimization wave number algorithm further optimizes the wave number sequence, and the algorithm can be divided into the following 4 steps.
Step 1: verifying the tolerance condition of each node in the wave number sequence w, and finding out the node n meeting the tolerance requirement1，n2，...nc}; if c is 0, turning to step 4;
step 2: computing node n1，n1，...ncThe corresponding minimum spacing s1，s1，...sc}; and look for s1，s1，...scThe node s corresponding to the minimum value in thek；
And step 3: removing s from the wave number sequence wk. If c is more than 1, turning to the step 1; if c is 1, then go to step 4;
and 4, step 4: and outputting an optimized wave number sequence.
S5: and judging whether the optimized wave number sequence is the same as the initial wave number sequence or not, if not, turning to S6, and if so, adding 1 to the number of wave number nodes and turning to S2.
S6: and outputting the final optimized wave number sequence.
Example 2
As is known, the resistivity anisotropy condition is more complex than the resistivity isotropy condition, and when the marine controllable source is evolving a wave number domain and time domain conversion, the resistivity anisotropy condition needs a relatively denser wave number sequence to obtain the Fourier transform calculation precision same as the resistivity isotropy. To illustrate the effectiveness and adaptability of the algorithm, the optimal wave number calculation example selects a more complex resistivity anisotropy case for discussion.
Referring to fig. 2, a structural diagram of a one-dimensional resistivity anisotropy model is shown. For comparing the accuracy of different wave number sequences, forward calculation is performed on different wave number sequences based on the model shown in fig. 2 as an example, and a seawater layer with the depth of 300m is assumed to be isotropic in resistivity, and the resistivity is 0.3 Ω m; the buried depth of the high-resistance thin layer with the thickness of 100m is 1 km; assuming that all underground media have resistivity main axis anisotropy (namely the resistivities in the x direction, the y direction and the z direction are different), setting the resistivity rho in the x direction of the surrounding rock and the resistivity rho in the high-resistance layer x1 omega m and 10 omega m respectively, and the resistivity ratios of the surrounding rock and the high-resistance layer in the x direction, the y direction and the z direction are the same (rho)x∶ρv∶ρz1: 4: 10). The horizontal electric dipole source with the survey line direction is positioned at a position 30m (the survey line direction y is 0m) right above the seabed base (0, 0), and 20 receiving stations are arranged on the seabed at equal intervals within the range from y being 0.5km to y being 10 km. The emission frequency was set to 0.25Hz and the emission current was set to 1A.
In the following simulation example, the initial wave number sequence is set to [10 ]-6，1]100 nodes with equal logarithmic spacing in the range are formed, and the error precision is set to be 0.2%. The wave number sequence is optimized by using the method for optimizing the controllable source electromagnetic simulation wave number sequence based on the elimination strategy, and the optimized wave number consisting of 41 nodes which are not uniformly distributed is finally obtained. 200 wave numbers ([10 ]) are set to be used-8，10]RangeInner logarithm equally spaced) to obtain a wave number domain simulation result as a reference solution.
Referring to fig. 3, the distribution of the initial wavenumber sequence, the initial sequence, the optimized sequence and the wavenumber sequence obtained by the conventional method is shown schematically. As can be seen from the figure, each node in the initial wave number sequence based on the least square fitting method is gathered to a section with a larger wave number (diamond line), because the wave number domain response changes more severely in the range, and the more dense node distribution can improve the calculation accuracy of the simulation result; the optimized solution obtained by the first optimization method is more sparse than the initial solution (square lines), thereby illustrating that the optimization algorithm can effectively eliminate redundant nodes to be aggregated; the optimized wave number sequence has the phenomena of sparse two ends and dense middle section, so that the response curve changes more smoothly at the two ends with larger and smaller wave numbers.
Referring to FIG. 4, the resulting spatial domain horizontal electric field component E is calculated for different wavenumber sequencesy(x, y, z), horizontal magnetic field component Hx(x, y, z) and a vertical electric field component EzAmplitude (fig. 4a), phase (fig. 4b) and amplitude relative error (fig. 4c), phase absolute error (fig. 4d) of (x, y, z). For convenience of comparison, the range [10 ] is also shown-6，1]Electromagnetic field response calculated by three conventional wave number sequences with inner logarithm equal interval, wherein the dotted line of diamond is horizontal electric field EyReference solution (wave number [10 ]-8，10]200 wave numbers with equally spaced range logarithms), the triangle point line, the cross point line and the square point line are respectively the wave numbers [10 ]-6，1]The range logarithms equally spaced 80, 70 and 60 nodes constitute the electromagnetic field response calculated for the wave number sequence. As can be seen from the figure, (1) when the wave number sequence is selected according to logarithmic equal intervals, the more the wave number (the smaller the interval), the smaller the error, the higher the numerical integration precision; (2) horizontal electric field component E calculated using optimized wave numbery(x, y, z), horizontal magnetic field component Hx(x, y, z) and a vertical electric field component EzThe amplitude error of (x, y, z) strictly meets the set error precision (0.2%), and the maximum value of the absolute error of the phase does not exceed 0.2 degrees; (3) the calculation precision of 41 wave number sequences obtained by utilizing the optimization algorithm provided by the patentThe degree is higher than the calculation accuracy of 60 wave numbers with logarithmic equi-spacing and is equivalent to the calculation accuracy of 70 wave numbers with logarithmic equi-spacing. Therefore, the wave number mathematical column optimization algorithm provided by the patent can effectively remove redundant wave numbers on the premise of ensuring the high precision of simulation results.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (4)
1. A controllable source electromagnetic simulation wave number sequence optimization method based on an elimination strategy is characterized by mainly comprising the following steps:
s1, initializing input variables including an initial wave number sequence and error precision;
s2, adjusting the positions of wave number sequence nodes based on a least square fitting method, and outputting a preliminary solution;
s3, eliminating redundant wave number at the minimum distance position by using the first optimized wave number algorithm;
s4, eliminating redundant wave numbers at positions with non-minimum spacing positions by using an optimized wave number algorithm II, and outputting an optimized wave number sequence;
s5, judging whether the optimized wave number sequence is the same as the initial wave number sequence or not, if not, turning to S6, if so, adding 1 to the number of wave number nodes, and turning to S2;
and S6, outputting the final optimized wave number sequence.
2. The elimination-strategy-based controllable-source electromagnetic simulation wave-number sequence optimization method of claim 1, wherein phi | (d-f (w)) | (| n silica) is calculated based on a least square fitting method2Is an objective function (where phi is the objective function of the optimized wave number; d ═ d1,d2,…,dN)TIs target data; n is the number of data; w ═ w (w)1,w2,…,wM)TThe wave number sequence is adopted, and M is the number of elements in the wave number sequence; f (w) is a model simulation response function), and optimization is carried out by solvingAnd solving the optimal solution of the objective function phi by using a Gauss-Newton method, namely adjusting the position of each node of the wave number sequence in the process and outputting an initial solution.
3. The method for optimizing a controllable-source electromagnetic simulation wave-number sequence based on an elimination strategy as claimed in claim 1, wherein the wave-number algorithm is optimized-based on the aggregation property of redundant nodes, two nodes with the minimum distance in the wave-number sequence are found, and the redundant nodes are eliminated under the condition of meeting the precision.
4. The elimination strategy-based controllable source electromagnetic simulation wave number sequence optimization method of claim 1, wherein the second optimization wave number algorithm is to eliminate redundant nodes at non-minimum spacing positions, judge and selectively eliminate each node in the wave number sequence one by one, and finally output the optimized wave number sequence.
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